Reflected UAS: Corrected Deterministic Stability and Direct CTMC Drift Calculation

Abstract:We analyze Reflected UAS routing for heterogeneous multi-server queues at fixed parameters under subcritical load. The deterministic surrogate is a reflected ODE on the nonnegative orthant, not the unconstrained drift equation. This reflected ODE has a unique boundary equilibrium characterized by a scalar consistency equation and a convex-potential representation; all trajectories converge to it. The older argument lifting deterministic Lyapunov descent to CTMC stability fails: the exact generator applied to the deterministic potential produces a boundary term absent from the reflected-ODE descent identity. We give a direct Foster-Lyapunov drift inequality for the CTMC using a weighted-quadratic function, bypassing the failed lift. At the benchmark parameter point, the boundary equilibrium matches the numerical attractor to machine precision, and the default Reflected UAS policy has lower mean queue length than UAS and JSSQ across independent seed blocks.

Performance (cs.PF); Artificial Intelligence (cs.AI); Probability (math.PR)

arXiv:2607.28688 [cs.PF]

(or arXiv:2607.28688v1 [cs.PF] for this version)

https://doi.org/10.48550/arXiv.2607.28688 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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